In conventional information processing systems, interconnections between system components generally function merely as communication pathways. In neural networks, however, the interconnections play a dominant role in the data processing scheme. The search for methods to achieve this interconnection intensive computation has led to the use of optical devices and networks in some applications. Holographic techniques, for example, are promising because of the potentially high capacity achievable through parallel processing of information. Volume holograms in particular provide a very compact method of storing informational interconnection patterns. Background and theoretical aspects of these techniques are described by D. Psaltis, D. Brady, K. Wagner in "Adaptive Optical Networks Using Photorefractive Crystals", APPLIED OPTICS, Vol. 27, No. 9, pp. 1752-59, May 1, 1988, and P. Yeh, T. Chang, P. Beckwith in "Real-time Optical Image Subtraction Using Dynamic Holographic Interference in Photorefractive Media", OPTICS LETTERS, Vol. 13, No. 7, pp. 586-88, July 1988. These articles are incorporated herein by reference.
In the most basic network having a plurality of input pattern elements, the output y(p) may be a function of the weighted sum of the input elements. Such a system can be used with a threshold function to dichotomize a set of patterns into two prescribed classes. More complex, multiple layered networks can be built up using this scheme as the basic building block. Extensions to multiple category pattern classification can be achieved simply by having a matrix of weights and a multiplicity of output units.
A simple learning algorithm for the output y(p) can be characterized by the update equation EQU w.sub.i (p+1)=w.sub.i (p)+m(p) x.sub.i (p),
where w.sub.i (p) is the i.sup.th weight at time p, x.sub.i (p) is the i.sup.th element of the pattern at time p, and m(p) is a multiplier that depends on the particular learning algorithm. For the perceptron learning algorithm, ##EQU1## Thus, for direct implementation of this type of algorithm, it can be seen that both additive and subtractive changes must be made to the weighting factors w.sub.i.
The basic components for an optical implementation of the network described above are an input device to convert the patterns into an appropriate format (for example, electrical to optical and incoherent to coherent), an interconnection device, and a thresholding device for the output. The function of the interconnection device in this system is to compute the inner product between the input pattern elements x.sub.i and the weight factors w.sub.i. This function can be performed by volume holograms in a way that is extendable to the multiple category case that requires multiple inner products.
In one example of an optical neural network, a holographic medium is placed at the Fourier plane of a lens. An input pattern is displayed in a spatial light modulator (SLM) placed at the front focal plane of the lens. The hologram is exposed with a reference plane wave and the pattern in the SLM. After development, a second pattern is loaded into the SLM. Light passing through the SLM and carrying the second pattern is diffracted by the hologram. The amplitude of the diffracted light is the inner product of the first and second patterns of the SLM. With two dimensional patterns a planar hologram is sufficient. However, with multiple categories where a number of different inner products must be computed simultaneously, the added dimension afforded by a volume hologram is preferable to spatial multiplexing of the planar hologram. Multiple category classification is achieved by an angular multiplexing of the volume hologram.
Photorefractive crystals are ideal for the holographic medium because of their dynamic nature. Crystals such as LiNbO.sub.3, BaTiO.sub.3, and SBN require relatively low optical intensity levels and therefore are very efficient as holographic media. The most efficient photorefractive crystals exhibit photosensitivity approaching that of photographic film.
Prior optical systems have employed photorefractive crystals for adaptive interconnections but have used incoherent erasure to achieve subtractive weight changes. In one known system, a photorefractive crystal is placed at the image plane of an SLM, and a movable piezoelectric mirror is used to provide either a coherent or an incoherent reference beam. For additive changes to the hologram, a coherent reference beam is provided so that the hologram is strengthened. For subtractive changes, the reference beam is made incoherent with respect to the object beam so that nonuniform incoherent erasure results. This method is roughly equivalent to providing a weight bias in which erasure results in subtraction. Incoherent erasure, however, does not take full advantage of the phase sensitive nature of holography. Therefore, a need exists for an adaptive optical neural network that exploits the coherent capability of holograms to provide both additive and subtractive weight change capabilities necessary for implementing learning algorithms.